Stitch image based on overlapping area

I have several images with overlapping edges (overlapping area between any two images ranges between 5% to 15%). The image below is a representative manual overlap of two sample images I'm working with. Which would be the most effective method to stitch them together and correct the differential brightness of the overlapping areas? (I was hopping to use something like Phase correlation and fast Fourier transform but I'm too new in image registration).